A Model for Shelled Micro-Bubble in Geometric Confinement under Acoustics Field

Abstract

A theoretical model to predict the dynamics of a shelled micro-bubble driven by acoustic field in a tubular geometric confinement is proposed in the present study. The model is derived from first principle and may not be considered as a variant of Rayleigh-Plesset solution. A semi-analytical model is derived in the form of an ordinary differential equation connecting all parameters involved. Results obtained are in agreement with the available experimental data. The model is further linearized to obtain expression for the forced resonant frequency, which is shown to depend on geometric parameter of confinement as D/ where D and L are the tube diameter and length, respectively. Further, linear viscous damping coefficient is also studied and is found that an overdamped or an underdamped state exist base on shelled micro-bubble size and parameters of geometric confinement (L and D). The state of damping clearly indicate when the shelled micro-bubble in confinement would respond linearly or non-linearly under the influence of acoustic field‎.